Development of a trajectory generation method for a five-axis NC machine

This paper presents a real-time trajectory generation method and control approach for a five-axis NC machine. The spatial trajectory of the tool of the five-axis machine is described by a ruled surface, and the differential motion parameters of the tool are obtained from the curvature theory of the ruled surface. The controller computes position, orientation, and the differential motion parameters of the tool within a specified sampling period. The Ferguson geometric modeling technique is used to represent the tool trajectory as a ruled surface. The proposed method produces a smoother part surface and requires substantially less machining time when compared to conventional off-line approaches. The real-time control approach, based on the curvature theory of a ruled surface, is believed to be an original contribution to the precise control of a five-axis NC machine.